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What Makes a Latent Space Shared? Direct and Recoverable Compatibility in Motion VAEs

Iago Brito, Walcy Rios, Lucas Fernandes, Kaiki de Oliveira, Arlindo Galvão Filho

arXiv:2610.17376v1cs.AIcs.CV

TL;DR

Different motion schemas can encode the same movement in different latent coordinates, so a shared backbone or prior alone may not make representations directly compatible. The paper compares recoverable correspondence, direct agreement, and decoder reuse in controlled HumanML3D views, finding that paired clips improve direct compatibility but do not ensure native-quality crossed decoding.

  • Problem

    Motion schemas differ in skeletons, coordinate systems, parameterizations, temporal resolutions, and preprocessing, while common representations or structural information do not settle how corresponding instances align in latent coordinates.

    Source: §1 · p. 1, §4.3 · p. 6

  • Method

    The study tests how cycles, marginal-alignment objectives, and explicit motion-pair anchors affect direct or calibrated clip and token correspondence across interfaces sharing a VAE backbone and prior.

    Source: §4.3 · p. 6

  • Results

    Identical inputs yielded 5.9–17.7% raw Recall@1 despite above 99.6% held-out CCA retrieval; 64 paired clips raised raw Recall@1 to 88.4–90.3% and paired-token cosine to approximately 0.82.

    Source: §1 · p. 2

  • Takeaways & Limitations

    A shared backbone or prior does not ensure directly compatible coordinates, and reducing measured marginal discrepancy does not establish schema invariance or paired compatibility.

    Source: §6.2 · p. 9, §7 · p. 10

    Crossed-decoding evidence is limited to the tested B→A setting, where Anchor-64 MPJPE remained 73.87–79.83 mm versus 43.38–44.45 mm natively.

    Source: §6.3 · p. 10, §7 · p. 10

Abstract

from arXiv · show

A shared latent space is often assumed to make representations from different schemas directly interchangeable, yet sharing parameters, dimensionality, or a prior does not determine how corresponding instances are expressed in latent coordinates. We show that this assumption conflates recoverable correspondence, direct compatibility, and decoder reuse. In a controlled multi-schema motion VAE on HumanML3D, even identical inputs yield only $5.9$--$17.7\%$ raw Recall@1 and $0.221$--$0.484$ paired-token cosine, despite correspondence being almost perfectly recoverable after linear calibration. Cycle consistency strengthens recoverability but still leaves direct retrieval and token agreement near zero. In contrast, only $64$ paired clips raise raw Recall@1 to $88.4$--$90.3\%$ and token cosine to approximately $0.82$, making most post-hoc alignment unnecessary, although crossed decoding remains substantially worse than native reconstruction. We further find that reducing measured marginal discrepancy does not imply schema invariance. These results show that a shared backbone or prior does not ensure directly compatible latent coordinates, while limited paired correspondence can substantially improve direct compatibility in the tested setting.

1 INTRODUCTION

The paper asks whether a shared learning objective makes different motion schemas directly interoperable, distinguishing direct coordinate agreement from correspondence recoverable through a transformation. In controlled HumanML3D views, shared-backbone training alone gives weak direct compatibility, while paired correspondence improves it without guaranteeing decoder reuse.

1 INTRODUCTION

  • The study asks what cross-schema compatibility a shared objective induces and what additional signals identify directly interoperable latent coordinates.Correspondence can be recoverable through a schema-specific transformation without direct coordinate compatibility, and compatible coordinates may still not suffice for another interface’s decoder.Source: §1 · p. 1
  • A minimal multi-schema VAE retains native schema parameterizations and connects them through schema-specific adapters to a shared encoder–decoder backbone with a common Gaussian prior.The controlled views derive from the same HumanML3D motions, making correspondence exact by construction.Source: §1 · p. 1
  • Compatibility is evaluated through pooled-vector retrieval, held-out retrieval after post-hoc alignment, synchronized token comparison, cross-schema decoding, and marginal alignment.Calibrated performance diagnoses recoverable correspondence, not intrinsically shared coordinates, and depends on the mapping family and correspondence budget.Source: §1 · p. 2
  • With identical inputs, raw Recall@1 is only 5.9–17.7% despite held-out CCA retrieval above 99.6%; 64 paired clips instead raise raw Recall@1 to 88.4–90.3% and paired-token cosine to approximately 0.82.Crossed decoding nevertheless remains markedly worse than native reconstruction.Source: §1 · p. 2

2 RELATED WORK

Prior work addresses motion-schema heterogeneity through common parameterizations or structural links between representations. Other research studies cycle consistency, distributional alignment, and identifiability, while this paper distinguishes the forms of compatibility they may leave unresolved.

2 RELATED WORK

  • Motion research has used common schemas or provided topology, semantic body-part correspondences, and paired motions to relate otherwise distinct representations.The paper instead asks what compatibility emerges from schema-specific interfaces trained through a shared latent backbone and prior.Source: §2 · p. 2
  • Cycle consistency can leave the intended intermediate correspondence unidentified, including through distribution-preserving automorphisms or preservation of source information without the intended mapping.Prior motion approaches combine cycle consistency with adversarial retargeting or latent-code constraints.Source: §2 · pp. 2–3
  • Distributional alignment does not specify individual sample correspondences, and latent identifiability depends on structural assumptions or paired observations.Representation comparisons also depend on the allowed transformations and downstream operation; the paper separates distributional similarity, recoverable correspondence, coordinate agreement, and decoder compatibility.Source: §2 · p. 3

3 LEARNING SETTING

The learning setting uses schema-specific interfaces to connect native motion representations to a shared VAE backbone. Training conditions share reconstruction and prior regularization but differ in whether and how they add cross-schema signals.

3 LEARNING SETTING

  • A minimal multi-schema VAE retains each schema’s native representation while schema-specific interfaces connect it to a shared latent backbone.The cross-schema training signal varies without changing the basic model construction.Source: §3 · p. 3

3.1 MULTI-SCHEMA MOTION REPRESENTATION

  • Controlled views are created from underlying motions with exact clip-level correspondence, even when one view discards information available in another.Inputs retain their native feature layouts and are standardized independently by schema.Source: §3.1 · pp. 3–4
  • Schema-specific adapters connect each representation to a shared encoder and decoder, returning decoded features to the originating schema.The framewise architecture preserves temporal length; token-level comparisons and cross-schema reuse require aligned frame times and a shared temporal grid.Source: §3.1 · p. 4
  • Deterministic comparisons use posterior-mean tokens; clip-level representations summarize their temporal means and population standard deviations, while token analyses compare synchronized steps before pooling.The clip summary’s standard deviation measures temporal variation of posterior means rather than posterior uncertainty.Source: §3.1 · p. 4

3.2 TRAINING OBJECTIVES

  • Every training condition includes native reconstruction and KL regularization toward a standard Gaussian prior, but this shared floor uses no pair identities to relate interface coordinate frames.The common floor jointly trains adapters and shared parameters.Source: §3.2 · p. 4
  • Cycle consistency decodes a sampled source code through another schema and re-encodes it, penalizing latent and motion reconstruction errors without identifying the intended target-schema motion.The intermediate sequence has no paired reconstruction target.Source: §3.2 · p. 5
  • Marginal objectives compare distributions of pooled sampled latents, while domain-classifier regularization discourages schema-predictive information without supplying motion correspondences.MMD uses distributional information rather than motion-pair identities.Source: §3.2 · p. 5
  • Paired anchors use symmetric InfoNCE to encourage each motion’s representation to score above representations of motions with different clip identities.Anchor is the only primary condition supplied with explicit motion-instance correspondence.Source: §3.2 · p. 5

4 CHARACTERIZING CROSS-SCHEMA LATENT COMPATIBILITY

A shared ambient latent space does not ensure corresponding motions are directly comparable or usable across decoders. The section distinguishes direct and recoverable correspondence, decoder compatibility, and the coordinate constraints imposed by training signals.

4.1 DIRECT AND RECOVERABLE CORRESPONDENCE

  • Direct clip retrieval, post-hoc recoverable correspondence, and synchronized token agreement are distinct compatibility properties, not consequences of sharing a latent space.Direct retrieval uses a fixed representation and similarity rule; recoverable correspondence requires post-hoc calibration, while token agreement measures paired posterior-mean tokens before pooling.Source: §4.1 · pp. 5–6

4.2 DECODER COMPATIBILITY

  • Decoder compatibility requires interface j's latent tokens to work directly with decoder Gi, a stronger and directional requirement than retrieval or token similarity.For lossy views, absent source-schema information can also limit crossed decoding; the Identical setting isolates latent-interface incompatibility most cleanly.Source: §4.2 · p. 6

4.3 COORDINATE AMBIGUITY AND TRAINING SIGNALS

  • Different schema-specific signed permutations can preserve native reconstruction while separating corresponding tokens, so relative coordinate frames matter for direct compatibility.Cycles constrain round trips, MMD and adversarial alignment act on latent marginals, and anchors provide explicit motion correspondences.Source: §4.3 · p. 6

5 EXPERIMENTAL DESIGN

The experimental design compares controlled views of the same HumanML3D motions across training conditions and evaluates direct agreement, calibrated correspondence, marginal structure, and decoder reuse. It uses held-out full-gallery retrieval and separate diagnostics for these properties.

5 EXPERIMENTAL DESIGN

  • Table 2 organizes controlled views of the same HumanML3D motions, with Schema A native HumanML3D except in Disjoint.The comparisons use paired views while varying the representation presented to each interface.Source: §5 · p. 6, Table 2 · p. 7

5.1 CONTROLLED SCHEMA COMPARISONS

  • The study uses 4,384 test clips from controlled HumanML3D views, with pair identities available for evaluation but withheld from Floor, Cycle, MMD, and Discriminator learning.Training uses 20,942 eligible clips; views range from identical and reordered inputs to feature-selected, temporally subsampled, and disjoint representations.Source: §5.1 · p. 7

5.2 DIRECT AND RECOVERABLE CORRESPONDENCE

  • Full-gallery cosine retrieval measures direct clip compatibility, while synchronized posterior-mean token cosine measures token agreement and fitted Procrustes, ridge, or CCA maps test recoverability.Maps are fitted on training correspondences and evaluated on the untouched test split; calibration ordinarily uses all 20,942 eligible pairs.Source: §5.2 · p. 7

5.3 TRAINING COMPARISONS AND DIAGNOSTICS

  • The design compares three-seed VAE results and nested Anchor budgets, separately testing marginal structure and directed Schema B-to-A decoder reuse.Marginal structure uses a held-out schema probe and fixed-kernel MMD; decoder reuse compares crossed and native decoding on 512 test clips using local MPJPE over 21 non-root RIC joints.Source: §5.3 · p. 8

6 RESULTS

Across the tested motion schemas, paired correspondence substantially improves direct latent compatibility, while unpaired objectives and shared training do not ensure it. Even strong direct compatibility does not guarantee native-quality crossed decoding.

6.1 SHARED TRAINING DOES NOT ENSURE DIRECT CLIP OR TOKEN COMPATIBILITY

  • 5.91%–17.72% raw Recall@1 under Floor, Identical contrasts with 99.64%–99.86% after CCA; paired-token cosine is 0.221–0.484 versus 0.015–0.019 for mismatched pairs.The CCA calibrations use all 20,942 eligible training clips, and ranges summarize three seeds rather than confidence intervals.Source: §6.1 · p. 8, §6 · p. 8
  • Rotations Floor yields 0.16%–1.64% raw retrieval and 95.78%–96.30% after CCA; across checkpoints, raw retrieval and paired-token cosine track closely (ρSpearman ≈0.98).Reordered also varies substantially by seed, with its 36.82% raw-retrieval seed accompanied by token agreement around 0.71.Source: §6.1 · pp. 8–9
  • With 256 Rotations training pairs, CCA retrieves approximately 67% from trained Floor representations versus about 7% from untrained random encoders; with 20,942 pairs, scores reach approximately 96% and 74%.Procrustes reaches approximately 82% for Floor versus 37% for random representations at the full budget, so large-budget CCA alone is not a standalone measure of representation quality.Source: §6.1 · p. 9

6.2 UNPAIRED CONSTRAINTS IMPROVE DIFFERENT PROPERTIES

  • Cycle reaches 94.25%–94.89% Procrustes and 99.16%–99.25% CCA retrieval on Rotations, while raw retrieval stays at 0.09%–0.16%.Paired-token cosine remains −0.025 to 0.026, near the mismatched reference.Source: §6.2 · p. 9
  • MMD with λm = 1 reduces MMD2 to 0.0061–0.0098, yet raw retrieval remains 0.23%–2.85% and schema-probe balanced accuracy is 99.95%–99.99%.The discriminator instead raises raw retrieval to 12.55%–44.14% while schema-probe accuracy remains 99.94%–100%.Source: §6.2 · p. 9

6.3 PAIRED CORRESPONDENCE IMPROVES DIRECT COMPATIBILITY BUT NOT NATIVE-QUALITY DECODER REUSE

  • 88.41%–90.33% raw Recall@1 follows from 64 paired clips, while Anchor-64 paired-token cosine reaches 0.824–0.826.The Rotations dose response reaches 62.00%–75.75% raw Recall@1 with 16 clips and 94.07%–94.98% with 256.Source: §6.3 · p. 9, Figure 2 · p. 10
  • The 64-pair result is established only for Rotations; full-pair Disjoint Anchor reaches 99.59%–99.73% raw retrieval despite no shared input channels.On Rotations, full-pair Anchor also achieves perfect raw retrieval while schema identity remains almost perfectly predictable.Source: §6.3 · p. 10
  • Despite strong Anchor-64 alignment, crossed MPJPE is 73.87–79.83 mm versus 43.38–44.45 mm natively in the tested B →A setting.A fitted linear token map provides little additional gain for Anchor-64.Source: §6.3 · p. 10, Figure 2 · p. 10

7 CONCLUSION

The conclusion distinguishes recoverable correspondence, direct compatibility, and decoder reuse, arguing that sharing a backbone, prior, or marginal statistics does not establish these properties. The appendix describes controlled HumanML3D views that retain native schema differences.

7 CONCLUSION

  • A shared backbone or prior does not ensure directly compatible latent coordinates, and better direct compatibility does not guarantee native-quality cross-decoder reuse.Marginal discrepancy and schema invariance likewise need not track either form of correspondence.Source: §7 · p. 10
  • The conclusions are limited to controlled HumanML3D views; low-pair alignment is established for Rotations, while calibrated recoverability depends on comparison family and correspondence budget.Source: §7 · p. 10

A.1 SPLITS AND CONTROLLED VIEWS

  • Evaluation uses all 4,384 test clips, including 2,192 original–mirror pairs, while training and validation use eligible clips of at least 64 frames.There are 20,942 eligible training clips and 1,300 eligible validation clips.Source: §A.1 · p. 13
  • The native HumanML3D representation is 263-dimensional, combining root features, joint positions, continuous 6D rotations, velocities, and foot contacts.Positions and rotations cover 21 non-root joints; velocities cover all 22 joints.Source: §A.1 · p. 13
  • Rotations shares input channels with native schema A, whereas Disjoint compares position and rotation features without channel overlap.Reordered permutes joint groups and feature blocks; Sparse retains 11 non-root joints and every second frame.Source: §A.1 · p. 13

A.2 ARCHITECTURE

The model connects schema-specific adapters to a shared framewise MLP encoder–decoder. Its implementation compares several training objectives and uses nested paired-identity budgets with a fixed checkpoint policy for limited-pair Anchor results.

A.2 ARCHITECTURE

  • Schema-specific input and output adapters connect to a shared framewise MLP encoder and decoder, with hidden width 256 and latent dimension 64.The model produces one latent token per input frame.Source: §A.2 · p. 13, Table 6 · p. 14
  • Training samples posterior noise independently at each frame, while reconstruction and auxiliary losses use sampled latents and representation evaluation uses posterior means.Reconstruction and analytical diagonal-Gaussian KL are averaged over frames and features or latent dimensions, respectively.Source: §A.2 · p. 14
  • The temporal-backbone robustness experiment replaces residual MLP blocks with kernel-size-5 Conv1D blocks, adding temporal context but increasing parameters from approximately 1.04M to 3.14M.The comparison is not parameter-matched.Source: §A.2 · p. 14

A.3 OBJECTIVE IMPLEMENTATION

  • Cycle training crosses interface directions on temporally aligned views; MMD compares pooled sampled latents, while a gradient-reversal classifier predicts schema identity.Anchor applies symmetric InfoNCE to paired windows from corresponding clips and updates both input adapters and the shared encoder.Source: §A.3 · p. 14

A.4 PAIR BUDGETS AND CHECKPOINT POLICY

  • Limited-pair Anchor uses nested budgets of 16, 64, 256, and 1,024 unique paired clip identities and selects the final checkpoint at 200,000 steps.All-pairs Anchor and unpaired conditions instead use validation-selected checkpoints unless otherwise stated.Source: §A.4 · p. 14

B EVALUATION AND CALIBRATION

The evaluation separates direct clip and token agreement from correspondence recovered by calibration, alongside diagnostics for schema separability, marginal discrepancy, and decoder compatibility. Results show that Cycle can improve calibrated correspondence without improving direct retrieval, while explicit pairing and calibration budget affect retrieval outcomes.

B.1 CLIP REPRESENTATIONS AND RETRIEVAL

  • Full-clip representations concatenate the temporal mean and standard deviation of posterior-mean latent tokens, and retrieval compares each schema B test clip with all 4,384 schema A test clips.Recall@1 is the primary metric; the correct match is the exact counterpart, and mirrored counterparts count as errors.Source: §B.1 · p. 15

B.2 DIRECT TOKEN AGREEMENT

  • Direct token-agreement evaluation compares synchronized posterior-mean tokens without pooling or fitted transformations, using paired-token cosine similarity, relative Euclidean distance, and token RMSE.A fixed mismatched-identity pairing provides a reference without true correspondence.Source: §B.2 · p. 15

B.3 TRAINING-ONLY CALIBRATION

  • Calibration fits Procrustes, ridge regression, or CCA on frozen representations using training correspondences, then applies the fitted comparison unchanged to test retrieval.Reduced-budget comparisons use nested paired identities.Source: §B.3 · p. 15

B.4 MARGINAL DIAGNOSTICS

  • Schema separability uses an independent logistic-regression probe, while cross-model MMD uses a fixed multi-bandwidth RBF kernel and an unbiased test-set U-statistic.Source: §B.4 · p. 15

B.5 DECODER AND TOKEN-MAP DIAGNOSTICS

  • Decoder compatibility compares native schema A reconstruction with decoding schema B posterior means through the same decoder; a separate ridge-map diagnostic uses 200,000 training-frame pairs.The token-map diagnostic uses substantially more paired identities than Anchor-64 and is not a matched-budget comparison.Source: §B.5 · p. 16

C.1 PER-SEED RETRIEVAL RESULTS

  • Tables 7 and 8 report individual training runs underlying the main-paper results, with post-hoc maps fitted to frozen representations using 20,942 eligible training correspondences.Source: §C.1 · p. 16, Table 7 · p. 16

C.2 DISJOINT-SCHEMA COMPARISONS

  • Full-pair Anchor achieves 100% Recall@1 across three seeds in the Rotations objective comparison, while Cycle improves calibrated correspondence without improving direct retrieval in the Disjoint setting.Full-pair Anchor achieves near-perfect direct retrieval in Disjoint, which does not establish low-pair behavior there.Source: §C.2 · p. 16, Table 8 · p. 17

C.3 CALIBRATION BUDGETS AND RANDOM FEATURES

  • With 256 Rotations pairs, CCA retrieves approximately 67% of counterparts from trained Floor representations and 7% from random encoders; with all 20,942 pairs, random-encoder retrieval rises to approximately 74%.Procrustes remains more selective to learned structure under the full calibration budget.Source: §C.3 · p. 17

C.4 RANKING AND SANITY CHECKS

The sanity checks show that calibration improves ranking where raw retrieval is weak, while simple normalization does not resolve direct incompatibility. Known-feature and shuffled-pair controls clarify what retrieval and calibration results can establish; synchronized token results retain the direct-versus-recoverable separation.

C.4 RANKING AND SANITY CHECKS

  • For Rotations Floor (seed 42), the correct counterpart’s median rank improves from 1,140 raw to 1 after Procrustes or CCA, while mean reciprocal rank rises from 0.011 to 0.889 and 0.980, respectively.Source: §C.4 · p. 18
  • Centering and standardization leave all Identical Floor seeds below 20% raw Recall@1; known-channel matching reaches 100% using root features and 99.8% using contacts.The known-feature controls use explicitly aligned input channels and do not demonstrate learned latent compatibility.Source: §C.4 · p. 18
  • Shuffling correspondence identities before calibration reduces retrieval to 0.00% for Procrustes and 0.02% for CCA, while mirror substitutions explain only a small fraction of raw retrieval errors.For Rotations Floor (seed 42), mirrors account for 45 of 4,370 raw errors.Source: §C.4 · p. 18

D.1 SYNCHRONIZED TOKEN AGREEMENT

  • Cycle leaves corresponding tokens close to the mismatched reference despite nearly perfect calibrated retrieval, whereas Anchor-64 substantially improves direct token agreement.This separation is not solely an effect of temporal pooling.Source: §D.1 · p. 18, Table 11 · p. 18

D.2 MARGINAL DISCREPANCY AND SCHEMA SEPARABILITY

On Rotations, marginal discrepancy, direct retrieval, and schema separability do not move together; checkpoint choice and paired-identity budget also qualify the measured comparison between Anchor and calibration.

D.2 MARGINAL DISCREPANCY AND SCHEMA SEPARABILITY

  • All evaluated models remain more than 99.9% schema-classifiable, while lower measured MMD does not establish schema invariance or paired compatibility.MMD regularization reduces discrepancy without improving direct retrieval; Full-pair Anchor achieves near-zero measured MMD and perfect direct retrieval yet retains almost perfect schema separability.Source: §D.2 · p. 18, Table 12 · p. 19

E.1 CHECKPOINT SENSITIVITY

  • Checkpoint selection affects the measured dose response, without consistently favoring the fixed-final or validation-selected policy.The primary limited-pair results use the fixed final checkpoint at 200,000 steps.Source: §E.1 · p. 19, Table 13 · p. 19

E.2 PAIR-BUDGET-MATCHED CALIBRATION

  • Anchor generally achieves stronger direct retrieval than post-hoc calibration at the same paired-identity budget, particularly with 16 and 64 pairs.The comparison matches unique paired identities, not optimization amount; the weak 16-identity window CCA result is not a general limitation of CCA.Source: §E.2 · p. 19, Table 14 · p. 19

E.3 PAIR-SUBSET AND LOSS SENSITIVITY

Across these experiments and analyses, paired supervision and cycle objectives affect different aspects of compatibility: direct retrieval, calibrated recovery, and decoder reuse do not necessarily coincide. The paper also specifies architectural, pooling, and dataset boundaries on these conclusions.

E.3 PAIR-SUBSET AND LOSS SENSITIVITY

  • Across three 64-identity subsets, raw Recall@1 ranges from 85.68% to 90.10%; across 256-identity subsets, it ranges from 94.32% to 95.26%.With 64 pairs, varying InfoNCE weight yields 89.55–90.44% raw Recall@1; paired MSE at 256 pairs yields 97.92% in single-seed experiments, not establishing general superiority.Source: §E.3 · p. 20

F.1 CYCLE COMPONENTS

  • Both cycle terms improve calibrated retrieval over Floor on Rotations, their combination gives the strongest recovery, and none produces substantial direct compatibility.This is a single-seed ablation and does not establish a general interaction between the terms.Source: §F.1 · p. 20, Table 15 · p. 20

F.2 TEMPORAL BACKBONE

  • The temporal-convolutional backbone preserves weak direct retrieval and strong calibrated correspondence under Floor and Cycle, while full-pair Anchor again achieves near-perfect direct retrieval.Because the TCN also increases capacity, this tests architecture robustness rather than isolating temporal context; the architectures are not parameter-matched.Source: §F.2 · p. 20, Table 16 · p. 20

G.1 DIRECT CROSSED DECODING

  • Anchor-64 reduces the gap between native and crossed decoding, but crossed decoding remains worse than the native path.At 256 and 1,024 paired identities, crossed MPJPE is 69.05 and 60.30 mm versus native errors of 44.51 and 43.75 mm, respectively, in single-seed results.Source: §G.1 · p. 21, Table 17 · p. 21

G.2 TOKEN-LEVEL CALIBRATION

  • Token calibration substantially improves crossed decoding for Floor and Cycle, but its improvement is small for Anchor-64.This is a functional recoverability diagnostic, not a matched-budget comparison, because token calibration uses substantially more paired identities than Anchor-64.Source: §G.2 · p. 21

H.1 FLOOR INVARIANCE AND ARCHITECTURAL SCOPE; H.2 STOCHASTIC CYCLES AND CORRESPONDENCE

  • Independent signed-permutation reparameterizations preserve the Floor objective only when the shared architecture can represent the transformed effective functions; stochastic cycles can still coexist with incorrect correspondence.The argument identifies an objective ambiguity under that architectural condition, not proof that all transformations are realizable or learned representations differ only by signed permutations.Source: §H.1 · p. 22, §H.2 · p. 22

H.3 POOLING AND COORDINATE COMPARISONS

  • Orthogonal mappings between pooled descriptors need not correspond to orthogonal mappings between latent tokens, so clip-level retrieval does not establish framewise coordinate or decoder agreement.Signed permutations are an exception; calibrated retrieval depends on the mapping family and pair budget.Source: §H.3 · p. 22

I LIMITATIONS AND FUTURE WORK

  • The experiments use controlled HumanML3D views with exact correspondence, not independently collected motion data with noise, temporal misalignment, or distribution shifts.Limited-pair alignment is demonstrated only for Rotations; Disjoint uses full-pair supervision, and decoder compatibility is evaluated only B→A.Source: I LIMITATIONS AND FUTURE WORK · p. 23

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